How to simulate fresnel lamps
EEVEE:

This is as soft as you could possibly get with EEVEE.
Unfortunately softness is &quot;hard coded&quot; so you can't change lamp distance to have more/less softness.
I have used the same method as you - Spot Lamp enclosed in a Cube. I've also parented Lamp to the Cube just to make ability to move/rotate them nicely.
Lamp settings:
Basically this are the only settings that have influence over the lamp softness. Not much to play with:

Softness to the max - 100, Bias to the minimum - 0.001 and Exponent is a matter of taste.
There is not much to explain here, but if you have more questions feel free to ask in comments.